Husmeier D. (1997): Modelling conditional probability densities with neural networks. PhD thesis. Department of Mathematics, King's College London, December 1997. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Modelling Conditional Probabilities with Network Committees: How .. - Husmeier (1998) (1 citation) (Correct)
.... ) E jD;q 0 = N X t=1 K X k=1 k (t) fi k 2 i y t Gamma (x t ; w k ) j 2 Gamma ln a k Gamma 1 2 ln fi k 2 (55) Taking the derivatives of U with respect to fi, a, and w, we arrive at the update equations (12) 13) and (14) 17 See, for instance, 2] 4] and [7]. 25 ....
Husmeier D. (1997): Modelling conditional probability densities with neural networks. PhD thesis. Department of Mathematics, King's College London, December 1997.
Modelling Conditional Probabilities with Network.. - Husmeier, Althoefer (1998) (1 citation) (Correct)
....posterior probability for the kth class or component of the mixture after observing the data point (x t ; y t ) and is computed on the basis of the current or old network parameters q. The new network parameters q = a 1 ; a K Gamma1 ; oe 1 ; oe K ; w) are given by [7] 3 oe 2 k = P N t=1 k (t) i y t Gamma (x t ; w k ) j 2 2 P N t=1 k (t) 2(ae Gamma 1) 11) a k = h P N t=1 k (t) i ( Gamma 1) N K( Gamma 1) 12) w = argmin w fU(w)g; U(w) 1 2 K X k=1 T X t=1 k (t)oe Gamma2 k h y t Gamma k (x t ; w) i 2 ....
Husmeier D. (1997): Modelling conditional probability densities with neural networks. PhD thesis. Department of Mathematics, King's College London, December 1997.
The Bayesian Evidence Scheme for Regularising.. - Husmeier Self-citation (Husmeier) (Correct)
.... Gamma fi ki 2 i y ti Gamma f ki j 2 3 5 k (t) 67) and, with (61) Psi(q; N X t=1 K X k=1 m X i=1 k (t) fi ki 2 i y ti Gamma f ki j 2 Gamma ln p k Gamma 1 2 ln fi ki 2 # (68) 15 See, for instance, Bishop, 1995) Dempster et al. 1977) and (Husmeier, 1998). 29 Since k (t) is binary and thus D k (t) E jD;q 0 = P i k (t) 1jD; q 0 j = k (t) equations (62) and (68) lead to U(qjq 0 ) N X t=1 K X k=1 m X i=1 k (t) fi ki 2 i y ti Gamma f ki j 2 Gamma ln p k Gamma 1 2 ln fi ki 2 # (69) Taking the ....
Husmeier, D. (1998). Modelling Conditional Probability Densities with Neural Networks. PhD thesis, Department of Mathematics, King's College London. http://www.ee.ic.ac.uk/research/neural/Husmeier.html.
The Bayesian Paradigm: second generation neural computing - Penny, Husmeier, Roberts (1999) Self-citation (Husmeier) (Correct)
....i=1 c i g i (x) T A i Gamma1 g i (x) 1.32) The moderated committee output is then given by z y MOD = g(K(sCOM )a COM ) 1. 33) For classification and regression networks trained by the evidence framework the mixing coefficients, c i , can be obtained from estimates of the model evidence [5]. For small data sets, however, the estimates of model evidence are unreliable. For this reason c i is often set to 1=M which is the approach adopted in this paper. 1.3 Example results The Tremor data set, collected by Spyers Ashby [6] is a two class medical classification problem consisting of ....
D. Husmeier. Modelling Conditional Probability Densities with Neural Networks. PhD thesis, Department of Mathematics, King's College London, 1998.
Bayesian Approaches to Gaussian Mixture Modelling - Roberts, Husmeier, Rezek, Penny (1998) (12 citations) Self-citation (Husmeier) (Correct)
....we assume that the posterior parameter distribution is sharply peaked around the maximum likelihood solution (implicit in the local quadratic or Laplace approximation) so we consider only small changes in the parameters, to which the set of posterior probabilities are largely insensitive. Husmeier [11] considers an expansion of the Hessian for the GMM in terms of the approximate Hessian (obtained by following the approximation taken here) and a series of perturbation terms. The latter are found (empirically) to be negligible. He notes, furthermore, that neglecting these terms is equivalent to ....
.... P K Gamma1 k=1 P (k) F P (k) Gamma N X n=1 1 P (x n ) P (x n j k) Gamma P (x n j K) 21) where k indexes from 1: K Gamma1) Taking differentials again with respect to P (k) as we will approximate the determinant of the Hessian from its diagonal components only (see [11]) gives 2 F P (k) 2 fi fi fi fi fi = N X n=1 P (k j x n ) P (k) Gamma P (K j x n ) P (K) 2 hence our approximation to the determinant of H p is jH p j = K Gamma1 Y k=1 N X n=1 P (k j x n ) P (k) Gamma P (K j x n ) P (K) 2 (22) Note ....
D. Husmeier. Modelling Conditional Probability Densities with Neural Networks. PhD thesis, Department of Mathematics, King's College, University of London, 1997.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC